This is Dave from York, PA, the owner of a very nice 1986.5 Supra (n/a of course) with 79,000 orig. mi.

A little history...
I've read just about everything on this website and have been able to correct a few minor problems.
1. I have no engine codes
2. The car idles well (cold at 1,100 rpm and warm at 700 rpm). I'm fairly sure this is correct.
3. Air Flow Meter was bad and was replaced. Tested with ohm meter.
4. was getting that fresh gas smell in the cabin so I disconnected the charcoal canister and sealed off the vacuum lines. Left the line from the gas tank open to prevent pressure from building up in the gas tank. (found this tip on this, or another web site, not sure) Works good.
5. Set timing per the online TSRM.
6. Added new spark plugs...Bosch Platinum...(are these bad plugs for this car?)
7. There are no air leaks between the AFM and throttle body.
8. I adjusted the TPS per the online TSRM.

Here's the issue...
The car runs well while cold, but when the car warms up I get what the TSRM calls muffler explosion (not backfire) on deceleration. The car is also very sluggish at normal operating temperature, but it idles without any problems.

The TSRM has many possible explanations for this condition. I would like to know what the most likely problem is, so that I don't waste time and money trying to fix.

when does it do the "muffler explosion"

i would suspect that there is unburnt fuel in the exhaust? bad plugs? i hear ngk are the best non platinum alternative
maybe the plugs aren't burning/sparking well enough to ignite all the fuel

what does the tsrm suggest... maybe it'll jog my memory and can pin point something

Here are what the TSRM says could be the problem for poor acceleration and muffler explosion (after fire)

POOR ACCELERATION:
High tension cord faulty???
Fuel system clogged???
EFI system problems???
Low compression???
Vacuum leaks: This has already been checked and there are no leaks.
Pulling air between AFM and throttle body: I have no problem here.
Ignition timing: Timing is correct.
Air cleaner clogged: Air cleaner is new
Spark Plugs faulty: Has new bosch plat. plugs
Engine Overheats: Not an issue.

MUFFLER EXPLOSION (after-fire)
EFI system problem???
Ignition timing: Timing is correct
Air cleaner clogged: Air cleaner is new.

well... take it for a run

then park it up... let it cool a bit so you can actually touch stuff lol
pull the easiest plug you can get to ;)
what is it firing like

to be honest i wouldn't use bosche... we're japanese cars... so we use japanese plugs... well that's my opinion anyhow heh

you still didn't mention when exactly the muffler explosion happens?
on boost.. off boost.. acceleration... deceleration... idle?

sounds like fuel injector clogged or sticking, bare in mind that the timeing is correct? have you had it scoped to be sure? another thing is spray the intake with brake cleaner well its running to see if you have a vacum leak, sometimes you cant hear it but its there, wireds? cap? rotor? look at all your ignision stuff make sure its all good, not half ass stuff, i got my car with 3 differant types of wires on it, pull the wires as the cars running make sure there all firing, do the basic stuff, look for compresion, look at the fuel pressues, you may have a fuel pump going south, make sure the pump holds pressue, hook up a gage and see if it drops after you turn the key off? if it dose that means fuels bleading back into the tank or into the engine threw a stuck injector.

Thanks for everyones help.

I was able to get the car running much better by replacing the spark plug wires, cleaning the throttle body/vacuum ports, and replacing a few pieces of questionable vacuum tubing.

I'm fairly sure the biggest problem was the #4 spark plug wire, the wire was kinked and I would bet that the wire's core and insulation was damaged.

isent that funny..........the guy i got my car off said the same thing about why he replaced just plug and wire to cyl 4..........odd ive not taken a really good look at my engine yet.............im working on the body right now.